Abstract

We define a new family [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i"/] of generating functions for w ∈ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i"/] which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions including symmetry, dominance and conjugation. We conjecture certain positivity properties in terms of a subfamily of symmetric functions called affine Schur functions. As applications, we show how affine Stanley symmetric functions generalize the (dual of the) k-Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur functions of Postnikov. Conjecturally, affine Stanley symmetric functions should be related to the cohomology of the affine flag variety.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1553-1586
Launched on MUSE
2006-12-11
Open Access
No
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